Kauppi et al. 10.1073/pnas.0608343103. |
Table 3. The percentage of forest production from plantations and the relative areas of plantations and natural forests to grow that production
Plantation production p | 25% | 33% | 50% | 75% | 90% | 100% |
Natural forest production (1-p) | 75% | 67% | 50% | 25% | 10% | 0% |
Plantation area | 14% | 20% | 33% | 60% | 82% | 100% |
Natural area | 86% | 80% | 67% | 40% | 18% | 0% |
Supporting Text
This information supports statements in the section, Industrial Harvest, Trade and Leakage and uses the framework and variables of the Forest Identity to support two statements, logically and in concrete quantities. The impact of exporting timber from a warm region of fast growth to a cool region of slow growth prompted the first statement. Growing plantations rather than natural forests prompted the second statement.
Warmer climate, faster growth
[Support for the statement, "The shift toward harvest in a region where density increases about twice as fast slowed the expansion of area to replace the growing stock by 17% or 3.1 M hectares (ha)."] This subject has its roots in the harvest of timber from warm, fast growing forests and its export to regions with cooler climates and slower growing trees.
We envision two forests, one with fast and one with slow growth. We vary the proportion harvested from the two forests and calculate the area to grow replacement stock. Our calculation relates the impact of volumes harvested to areas that sustain the forests by growing replacements for the harvested volumes. Let,
V' = m3 /yr harvested. Note this is neither the standing volume V = A ´ D of growing stock in a nation nor the relative change v of growing stock. Instead V' is the absolute m3 of the annual harvest from fast plus slow forests.
p
= dimensionless proportion of harvest V' from the region with the faster growth, which we define as a faster increase of density.D'2 and D'1 m3/ha/yr = density increase, where D'2 > D'1. Note that D' is the annual increase m3/ha/yr of D and not the standing growing stock D m3/ha in the equation V = A ´ D. Neither is D' the relative increase d of D.
A2 + A1 = the hectares of the faster and the slower growing forests to sustain themselves by matching the harvest V'.
Then, the volume of harvest that must be replaced by growth is
V' m3/yr = V'2 + V'1 = A2 ha ´ D'2 m3/ha/yr + A1 ´ D'1
The fraction of the harvest taken from the fast-growing forest is
p
dimensionless = V'2/ (V'2 + V'1) = A2 ´ D'2 / (A2 ´ D'2 + A1 ´ D'1)The area of fast-growing forest to replace the harvest from it is
A2 ha = p V'/D'2, dimensionless ´ m3/yr / (m3/ha/yr)
The area of slow growing forest to replace the harvest from it is
A1 ha = (1-p) V'/D'1
Hence the sum of the two areas in ha is
A2 + A1 ha = V' [(1-p)/ D'2 + p/ D'1]
Or the sum of the areas relative to harvest V' is
(A2 + A1)/ V' ha/(m3/ yr) = [(1-p)/D'2 + p/D'1]
Illustrate by the area spared by the shift in harvest from the north to the south region of the U. S. as reported by Smith et al. (1). The m3/ha/yr density increases were equated with the reported net growth plus removals from the ha of timberland. In the north and south in 2002, D'2 = 7.4, and D'1 = 3.6 m3/ha/yr. From 1976 to 2001, the annual harvest V' increased from 260 to 362 M m3. If p remained at its 1976 value while harvest increased from 260 to 362 M m3, the calculated A1+A2 to replace it would have spread by 17.8 M ha. But during 1976 to 2001, the fraction p harvested from the faster growing, southern forests rose 0.32%/yr, decreasing the area per harvested volume, (A1+A2) / V' from 174 to 165 ha per thousand m3. Because the greater harvest of the faster growing forest increased p and decreased the area per harvested volume, however, the area A1+A2 was 14.7. The difference between the 1976 value of p and its actual value in 2001 decreased area A1+A2 from 17.8 to 14.7 M ha, a difference of 3.1 M ha or 17%. In short, one can say that shifting harvest to faster growing forests spared 3.1 M ha, 17% of the impact of more harvest in 2001 than in 1976.
Plantations, faster growth
[Support for the statement, "Expansion of plantations is expected to lower the percentage of wood production volume from natural forests from the present 67% to 50% by 2025 and 25% of production by 2050 (27). Consider the entire decrease from 67% to 25% natural production and the 33% to 75% increase of plantation production that caused it. Logically, lowering the volume harvested from natural forests from 67% to 25% will shrink the natural area to match their production from 80% down to 40% of the total area to match all production."]
The literature abounds in projections of production from plantations versus that from natural forests. To understand the impact of production on natural forests, however, one wants to know the percentage of area of natural forests versus plantations to replace the production. Let,
V' m3 /yr = harvested from plantations and natural forests,
p
dimensionless = proportion of production V' from the plantations,D'2 and D'1 m3/ha/yr = density increase in plantations and natural forests.
A2 + A1 ha = areas of plantations plus natural forests to grow, replace or match harvest V'.
Then, the total harvest is
V' m3/yr = V'2 + V'1 = A2 ha ´ D'2 m3/ha/yr + A1 ´ D'1,
while the fraction of harvest from plantations is
p
dimensionless = V'2/ (V'2 + V'1) = A2 ´ D'2 / (A2 ´ D'2 + A1 ´ D'1).1/p dimensionless = A2 ´ D'2/ (A2 ´ D'2) + A1 ´ D'1/(A2 ´ D'2)
= 1 + A1 ´ D'1/ (A2 ´ D'2).
A1 ´ D'1/ ((A2 ´ D'2) dimensionless = (1-p)/p.
A1/A2 + A2/A2 dimensionless = D'2/ D'1 ´ [(1-p)/p] + 1,
The fraction of the replacement area that is plantation is
A2/ (A1 + A2) dimensionless = {D'1/ D'} ´ [(1-p)/p] + 1}-1
The impact on natural forests is 1 minus the fraction of the replacement area that is plantations.
The ratio D'2/ D'1 is generally >1 and thus D'1/ D'2 < 1. Up to about p = 60% the fraction of the area A2/ (A1 + A2) to match plantation production expands more slowly than p rises, as an example illustrates.
Illustrate with growth rates from Indian plantations (2). Because Lal and Sing report that the plantations add density about twice as fast as natural forests, let D'2/D'1 = 2. Calculate the consequences of 25% production from plantations, the present 33%, and projections of 50% and 75% (3). In Table 1, consider the present case of p = 33% plantation production and corresponding 67% natural forest production. Plantations occupying only 20% of the area produce 33% of the wood, while natural forests still require fully 80% of the area to match only 67% of the wood production. The percentage of natural area to grow its fraction of production does fall more slowly than its percentage of production until p from plantations reaches about 60%, but then the percentage of natural area to grow its fraction plummets.
1. Smith WB, Miles PD, Vissage JS, Pugh SA (2002) Forest Resources of the United States General Tech. Rep. NC-241 (U.S. Department of Agriculture, Forest Service, North Central Research Station, St. Paul, MN).
2. Lal M, Singh R (2000) Environ Monit Assess 60:315-327.
3. Sohngen B, Mendelsohn R, Sedjo R (1999) Am J Agr Econ 81:1-13.